1. Technical Field
The present invention relates to a method and apparatus for the compensation of S-parameters of a passive circuit, and more particularly to a method to compensate S-parameters to satisfy passivity.
2. Description of Related Art
S-parameters are transmission and reflection coefficients for a circuit computed from measurements of voltage waves traveling toward and away from a port or ports of the circuit. Further, the S-parameters are related to frequency. In general, S-parameters are expressed either in terms of a magnitude and phase or in an equivalent form as a complex number having a real part and an imaginary part. Referring to FIGS. 1 and 2, a passive circuit 10 includes a port 11 and a port 12. A set of four S-parameters, namely S11, S12, S21, and S22 each represented by a complex number, provide a complete characterization of the performance of the two ports 11, and 12 of the passive circuit 10 at a single frequency. These S-parameters form an S-parameter matrix. Because the circuit 10 is a passive circuit, the S-parameter matrix should satisfy passivity: real (eigenvalue[E−S×S′])≧0. It means that the real part of the eigenvalue of the matrix [E−S×S′] is not smaller than 0. The matrix S′ is a complex conjugate transposed matrix of the S-parameters matrix. However, in many instances, the measured S-parameters do not satisfy passivity for many different reasons, such as directivity and crosstalk related to signal leakage, source and load impedance mismatches related to reflections, and so on.
What is needed, therefore, is a method to compensate for the S-parameters of a passive circuit to satisfy passivity.